Although there may be conceptual differences between the two approaches http:// vs ws://, apparently, both result in similar outcomes.
Refer to the "environ" variable that is received as an argument by the "connect" handler (quoted from documentation: "the connect handler receives environ as an argument, with the request information in standard WSGI format, including HTTP headers.").
Print the value of "environ" when using ws:// vs http://. You will see that this variable stores a similar value in both cases.